CAIE S1 2004 June — Question 6

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2004
SessionJune
TopicTree Diagrams
TypeRepeated trials until stopping condition

6 When Don plays tennis, \(65 \%\) of his first serves go into the correct area of the court. If the first serve goes into the correct area, his chance of winning the point is \(90 \%\). If his first serve does not go into the correct area, Don is allowed a second serve, and of these, \(80 \%\) go into the correct area. If the second serve goes into the correct area, his chance of winning the point is \(60 \%\). If neither serve goes into the correct area, Don loses the point.
  1. Draw a tree diagram to represent this information.
  2. Using your tree diagram, find the probability that Don loses the point.
  3. Find the conditional probability that Don's first serve went into the correct area, given that he loses the point.